Tikz-cd arrow bending and loop for indicating that portion of diagram commutes

I am trying to get the arrow from $R$ to $R[x]$ to cooperate with me and go alongside the LHS of the picture.

Here is my MWE:

\begin{tikzcd}
& R \arrow[d, "f"] \arrow[ld, "\phi"', hook'] \arrow[rd, "\phi", hook] \arrow["i", hook', bend right=135]{dd} &  \\
R\left\lbrack\frac{1}{r}\right\rbrack \arrow[r, "\exists!F", two heads, dashed, hook] & {\frac{R[x]}{(rx-1)}} \arrow[r, "\exists!G", two heads, dashed, hook] & R\left\lbrack\frac{1}{r}\right\rbrack \\
& {R[x]} \arrow[u, "\pi", two heads] \arrow[ru, "g"'] &
\end{tikzcd}


I'd also like to know how to get the spiral that indicates that the diagram commutes inside the top left and bottom right triangles. See, for example, the below.

After seeing your figure (sorry did not read carefully enough! it is very dark in our burrow;-).

\documentclass{article}
\usepackage{tikz-cd,amsmath}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\begin{tikzcd}[execute at end picture={
\draw[{Hooks[width=+0pt 10.8,length=+0pt 3.6,harpoon,line cap=round]}->]
(\tikzcdmatrixname-1-2) to[out=175,in=185,looseness=3]
node[midway,left]{$i$} (\tikzcdmatrixname-3-2);
\draw[-{Latex[bend]},thick] ([xshift=-0.35cm,yshift=0.45cm]\tikzcdmatrixname-2-2)
arc(0:340:0.2);
\draw[-{Latex[bend]},thick] ([xshift=-0.45cm,yshift=-0.45cm]\tikzcdmatrixname-2-2)
arc(20:360:0.2);
\draw[-{Latex[bend]},thick] ([xshift=0.55cm,yshift=-0.45cm]\tikzcdmatrixname-2-2)
arc(20:360:0.2);
}]
& R \arrow[d, "f"] \arrow[ld, "\phi"', hook'] \arrow[rd, "\phi", hook] &  \\
R\left\lbrack\frac{1}{r}\right\rbrack \arrow[r, "\exists!F", two heads, dashed, hook] & {\frac{R[x]}{(rx-1)}} \arrow[r, "\exists!G", two heads, dashed, hook] & R\left\lbrack\frac{1}{r}\right\rbrack \\
& {R[x]} \arrow[u, "\pi", two heads] \arrow[ru, "g"'] &
\end{tikzcd}
\end{document}


• @nick5435 I added a hook (which I looked up in tikzlibrarycd.code.tex). Is this the hook you're after?
– user121799
Commented Dec 4, 2018 at 17:39
• This did the trick: \draw[left hook->] (\tikzcdmatrixname-1-2) to[out=150,in=185,looseness=3] node[midway,left]{$i$} (\tikzcdmatrixname-3-2);}] Just had to do \usetikzlibrary{arrows} Commented Dec 4, 2018 at 17:40